Low energy hadronic contribution to the QED vacuum polarization

Abstract

Recent improvements in the low energy e e ÿ annihilation data and their influence on the determination of the hadronic contribution to the running of the QED fine structure constant at m Z are discussed. Using CMD-2 and KLOE measurements in the region we obtain 5 had s 0:02 758 0:00 035 at s m 2 Z . DOI: 10.1103/PhysRevD.72.057501 PACS numbers: 13.85.Lg, 13.66.Jn, 12.15.Lk In the year 2001, we published an updated evaluation of the hadronic contribution to the running of the QED fine structure constant [1], based on a dispersion integral using a parametrization of the measured cross section of e e ÿ ! hadrons. We obtained a hadronic contribution of 5 had s 0:02 761 0:00 036 at s m 2 Z . Our parametrization in the c.m. energy region of the , the contribution of the ÿ final state from threshold to 1.8 GeV, was based on a pion form factor parametrization obtained by the CMD-2 Collaboration which used results of their measurements in the c.m. energy region between 0.61 and 0.96 GeV at the VEPP-2M collider [2]. The overall uncertainty of the region integral, including the statistical uncertainty, was 2.3% (that of ÿ ee in [2]) in our analysis.Since then, the CMD-2 Collaboration improved the treatment of radiative corrections twice. An intermediate improvement has appeared in the published document [3] and an additional improvement has become available in 2004 [4]. We have concluded that the most recent CMD-2 results imply only a small change in the estimate of the hadronic contribution [5].Recently, the KLOE Collaboration [6] has measured the cross section of e e ÿ ! ÿ with high statistical accuracy in small energy bins using the ''radiative return'' from the resonance to the in the ÿ mass range between 0.59 and 0.97 GeV.We have been repeatedly asked to update our previous analysis and to comment on and quantify the influence of recent low energy measurements by KLOE and CMD-2 on our results. We find that the actual change turns out to be very small. Thus, we have decided to submit this work as a brief report. To the extent that this report is an update of a previously published article, the choice is not to unnecessarily repeat the discussion for energy regions which did not change.In our 2001 analysis, we used the parametrization of the pion form factor obtained by the CMD-2 Collaboration.The contribution of the new results on 5 had m 2 Z is now obtained by direct integration between measured KLOE and CMD-2 data points separately. For CMD-2 we use the ''bare'' cross section and for KLOE the pion form factor data. These are quantities in which the vacuum polarization corrections have been removed. The small contribution from lower and higher energies, not covered by new data, is evaluated as previously using the CMD-2 parametrization of the pion form factor. We treat the systematic uncertainties as fully correlated between different c.m. energies within the CMD-2 experiment. For the integration of the KLOE data, we constructed a covariance matrix based on the statistical covariance matrix with the addition of fu...

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